Journal of Statistical Physics

, Volume 125, Issue 2, pp 411–453

Large Deviations for Non-Uniformly Expanding Maps


    • Instituto de MatemáticaUniversidade Federal do Rio de Janeiro
    • Centro de Matemática da Universidade do Porto
  • M. J. Pacifico
    • Instituto de MatemáticaUniversidade Federal do Rio de Janeiro

DOI: 10.1007/s10955-006-9183-y

Cite this article as:
Araújo, V. & Pacifico, M.J. J Stat Phys (2006) 125: 411. doi:10.1007/s10955-006-9183-y


We obtain large deviation bounds for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average tends to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states.


non-uniform expansionphysical measureshyperbolic timeslarge deviations

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© Springer Science+Business Media, Inc. 2006